I post this here as a possible solution for those who are experiencing a similar behavior.
I migrated a bunch of ESP8266/ESP8285 devices from Tasmota to ESPHome, but all disconnected from HA Core every couple of minutes or so.
I solved this issue on all those devices at once by migrating to ESPHome-dev (1.15.0-dev).
Just to give an idea, this is what the history shows forone of those devices, a RGBWW bulb. The red line is the reboot following the migration to ESPHome 1.15.0-dev
Add the esphome repository as the link above says. When you go to the add-on store you will see three versions of esphome. One of them is the dev version. If you are currently running the standard version stop it before starting the dev version. You can’t run both at the same time.